Place the broccoli stalk batons on a cutting board. Use a vegetable peeler to shave them into paper-thin strips, transferring them to a serving bowl as you work.

Tear any large leaves into bite-size pieces; add the leaves to the bowl, along with the oil and lime juice. Season with salt and pepper to taste; toss to coat evenly, then gently fold in the cheese.

Serve right away.

NOTE: To make broccoli batons, first remove the stalks at the base of the florets, then trim off the tough exterior of the stalks. Trim each stalk, rolling it on a flat side, to form a long, rectangular piece.